Mixed H2/H∞ filtering

The authors consider the problem of finding a filter or estimator that minimizes a mixed H₂/H_∞ filtering cost on the transfer matrix from a given noise input to the filtering error subject to a H_∞ constraint on the transfer matrix from a second noise input to the filtering error. This problem can be interpreted and motivated in many different ways-for instance, as a problem of optimal filtering in the presence of noise with fixed and known spectral characteristics subject to a bound on the filtering error due to a second noise source whose spectral characteristics are unknown. It is shown that one can come arbitrarily close to the optimal mixed H₂/H_∞ filtering cost using a standard Luenberger estimator. The problem of finding a suitable Leunberger estimator gain can be converted into a convex optimization problem over a subset of real matrices of dimension n×(n+1)/2+n×p, where n is the state dimension and p the number of measurements